Does the instruction in Transition Mathematics provide an opportunity for students to learn the benchmark ideas and skills?

Numerous sightings were analyzed to determine the instructional criteria ratings for Transition Mathematics. The following chart provides a typical example of the sightings that were analyzed to determine each criterion rating. Looking at these sightings will provide a picture of the overall instructional guidance provided in the textbook.

TYPICAL SIGHTING CHART  pdficon.gif (224 bytes)(Adobe PDF document)

The graph below depicts major strengths and weaknesses in the overall instructional guidance provided by Transition Mathematics. It does so by showing the average score Transition Mathematics received on each of the 24 instructional criteria, across all six of the benchmarks used for the evaluation.

INSTRUCTION HIGHLIGHTS CHART  pdficon.gif (224 bytes)(Adobe PDF document)


Overall, analysts rated Transition Mathematics as unsatisfactory in helping students achieve the number, geometry, and algebra benchmarks used for the evaluation. The following describes the seven instructional categories and their criteria and summarizes the analysts’ justification for their ratings for Transition Mathematics.


Instructional Category I

Identifying a Sense of Purpose
Part of planning a coherent curriculum involves deciding on its purposes and on what learning experiences will likely contribute to achieving those purposes. Three criteria are used to determine whether the material conveys a unit purpose and a lesson purpose and justifies the sequence of activities.

Although most of the activities are consistent with the purpose of the chapter, it is not clear that they would be interesting or motivating to students. Teachers are provided with notes about the introductions but are given no direction regarding discussions or opening activities that relate to the purpose. The text provides end-of-section questions for self-progress checks that relate to the overall purpose of the unit. Each section has the same components: introductory comments with a picture, diagram, graph, or chart; examples that lead to the development of specific problem-solving algorithms; and practice problems that address the specific skills/strategies just developed. There is no stated rationale for the sequence of activities.


Instructional Category II

Building on Student Ideas about Mathematics
Fostering better understanding in students requires taking time to attend to the ideas they already have, both ideas that are incorrect and ideas that can serve as a foundation for subsequent learning. Four criteria are used to determine whether the material specifies prerequisite knowledge, alerts teachers to student ideas, assists teachers in identifying student ideas, and addresses misconceptions.

Transition Mathematics rarely notes the prerequisite skills that students are assumed to have mastered and only does so superficially. Error Alerts provide teachers with general ideas that students might have about specific concepts or skills. Most of these alerts also clarify or explain accurately where students may have difficulties. Although the text often provides information that would allow teachers to identify student ideas before teaching a topic, it seldom provides suggestions or tools that would help teachers get information about these ideas directly from students. Only a limited number of activities directly address students’ common ideas or misconceptions.


Instructional Category III

Engaging Students in Mathematics
For students to appreciate the power of mathematics, they need to have a sense of the range and complexity of ideas and applications that mathematics can explain or model. Two criteria are used to determine whether the material provides a variety of contexts and an appropriate number of firsthand experiences.

There are numerous activities that directly address the ideas in the benchmarks; however, only a few of them deviate from pencil and paper or calculator activities. There are many opportunities for students to apply the skills in the benchmarks through problem solving, but few questions address when and why students should do procedures. There are a variety of skill development activities, but few of them would be meaningful or interesting to most students.


Instructional Category IV

Developing Mathematical Ideas
Mathematics literacy requires that students see the link between concepts and skills, see mathematics itself as logical and useful, and become skillful at using mathematics. Six criteria are used to determine whether the material justifies the importance of benchmark ideas, introduces terms and procedures only as needed, represents ideas accurately, connects benchmark ideas, demonstrates/models procedures, and provides practice.

While each section has some kind of introductory paragraph, these are brief and often fail to develop a comprehensible argument for why the mathematics makes sense. New terms are introduced in bold face at the beginning of sections with formal definitions and principles that students use immediately. Representations of concepts are shown through examples that would likely be comprehensible to students. Connecting concepts are presented at the beginning of each section where students are shown a strategy for applying the concepts and then given the opportunity to practice with applications. There are a sufficient number of practice exercises, although few of them are novel or use interesting situations.


Instructional Category V

Promoting Student Thinking about Mathematics
No matter how clearly materials may present ideas, students (like all people) will devise their own meaning, which may or may not correspond to targeted learning goals. Students need to make their ideas and reasoning explicit and to hold them up to scrutiny and recast them as needed. Three criteria are used to determine whether the material encourages students to explain their reasoning, guides students in their interpretation and reasoning, and encourages them to think about what they’ve learned.

The examples that ask the students to explain how to do a procedure fail to require students to explain their thinking or reasoning about why the procedure works. Transition Mathematics includes many examples showing step-by-step procedures for solving problems; however, it does not guide student interpretation and reasoning about the procedure or steps along the way. Exercises, reviews, and self-tests encourage students to think about what they’ve learned, but these are mainly focused on the skills benchmarks. There are few reviews and self-tests for concepts benchmarks.


Instructional Category VI

Assessing Student Progress in Mathematics
Assessments must address the range of skills, applications, and contexts that reflect what students are expected to learn. This is possible only if assessment takes place throughout instruction, not only at the end of a chapter or unit. Three criteria are used to determine whether the material aligns assessments with the benchmarks, assesses students through the application of benchmark ideas, and uses embedded assessments.

Assessment items for both the skills and concepts benchmarks are available; however, fewer items address the substance of the conceptual benchmarks. Even though the material includes several types of assessment items, the applications are mainly routine calculations done with pencil and paper. Embedded assessments are present, but they do not go beyond the students’ initial responses, and there are no suggestions to teachers for modifying or adapting learning activities based on how students perform.


Instructional Category VII

Enhancing the Mathematics Learning Environment
Providing features that enhance the use and implementation of the textbook for all students is important. Three criteria are used to determine whether the material provides teacher content support, establishes a challenging classroom, and supports all students.

Content information provided for teacher learning is effective for the number benchmarks but not for the geometry and algebra benchmarks. Transition Mathematics provides minimal help to the teacher in creating a classroom environment with opportunities for students to express or explore their own ideas. There are few suggestions for encouraging or adapting to an individual student’s creative thinking. There are many pictures of women and minorities, and activities are provided for students who have difficulties with English as well as students who are advanced.

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